Wang-Ball曲线的扩展

An Extension of Wang-Ball Curve

提出了带形状参数的n次Wang-Ball调配函数,它是n次Wang-Ball基函数的扩展,它具有与n次Wang-Ball基函数相似的性质。基于给出的调配函数,构造了带形状参数的多项式曲线。参数λ具有明确的几何意义,当λ增大时,曲线将逼近于控制多边形,当λ=0时,即退化为n次Wang-Ball调配函数,它为曲线设计提供了一种有效的方法。

In this paper, a class of blending functions of n degrees is presented. It is the extension of the Wang- Ball functions of n degrees, It has the similar properties with the n-degree Wang-Ball curves. Based on the blending functions, the polynomial curves with a shape parameter are constructed. By changing the value of the shape parameters, the approaching degree of the curves to their control polygons can be adjusted. These curves converge to n-degree Wang-Ball curves then. The presented method is useful for the curve design.